A complex adaptive systems approach to the kinetic folding of RNA

The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base pairs engage in local stacking interactions that determine the probabilities (or fitnesses) of possible SRs. Meanwhile, selection operates at the level of SRs; an autonomous stochastic process periodically (i.e., from one time step to another) selects a subset of possible SRs for realization based on the fitnesses of the SRs. Using examples based on selected natural and synthetic RNAs, the model is shown to qualitatively reproduce characteristic (nonlinear) RNA folding dynamics such as the attainment by RNAs of alternative stable states. Possible applications of the model to the analysis of properties of fitness landscapes, and of the RNA sequence to structure mapping are discussed.Comment: 23 pages, 4 figures, 2 tables, to be published in BioSystems (Note: updated 2 references

Techniques for modeling and analyzing RNA and protein folding energy landscapes

RNA and protein molecules undergo a dynamic folding process that is important to their function. Computational methods are critical for studying this folding pro- cess because it is difficult to observe experimentally. In this work, we introduce new computational techniques to study RNA and protein energy landscapes, includ- ing a method to approximate an RNA energy landscape with a coarse graph (map) and new tools for analyzing graph-based approximations of RNA and protein energy landscapes. These analysis techniques can be used to study RNA and protein fold- ing kinetics such as population kinetics, folding rates, and the folding of particular subsequences. In particular, a map-based Master Equation (MME) method can be used to analyze the population kinetics of the maps, while another map analysis tool, map-based Monte Carlo (MMC) simulation, can extract stochastic folding pathways from the map. To validate the results, I compared our methods with other computational meth- ods and with experimental studies of RNA and protein. I first compared our MMC and MME methods for RNA with other computational methods working on the com- plete energy landscape and show that the approximate map captures the major fea- tures of a much larger (e.g., by orders of magnitude) complete energy landscape. Moreover, I show that the methods scale well to large molecules, e.g., RNA with 200+ nucleotides. Then, I correlate the computational results with experimental findings. I present comparisons with two experimental cases to show how I can pre- dict kinetics-based functional rates of ColE1 RNAII and MS2 phage RNA and their mutants using our MME and MMC tools respectively. I also show that the MME and MMC tools can be applied to map-based approximations of protein energy energy landscapes and present kinetics analysis results for several proteins

Major Subject: Computer ScienceTECHNIQUES FOR MODELING AND ANALYZING RNA AND PROTEIN FOLDING ENERGY LANDSCAPES

Major Subject: Computer Scienceiii Techniques for Modeling and Analyzing RNA and Protein Folding Energ

Mechanically probing the folding pathway of single RNA molecules

We study theoretically the denaturation of single RNA molecules by mechanical stretching, focusing on signatures of the (un)folding pathway in molecular fluctuations. Our model describes the interactions between nucleotides by incorporating the experimentally determined free energy rules for RNA secondary structure, while exterior single stranded regions are modeled as freely jointed chains. For exemplary RNA sequences (hairpins and the Tetrahymena thermophila group I intron), we compute the quasi-equilibrium fluctuations in the end-to-end distance as the molecule is unfolded by pulling on opposite ends. Unlike the average quasi-equilibrium force-extension curves, these fluctuations reveal clear signatures from the unfolding of individual structural elements. We find that the resolution of these signatures depends on the spring constant of the force-measuring device, with an optimal value intermediate between very rigid and very soft. We compare and relate our results to recent experiments by Liphardt et al. [Science 292, 733-737 (2001)].Comment: 10 pages, 8 figures, revised version, to be published in Biophys.

SIMS: A Hybrid Method for Rapid Conformational Analysis

Proteins are at the root of many biological functions, often performing complex tasks as the result of large changes in their structure. Describing the exact details of these conformational changes, however, remains a central challenge for computational biology due the enormous computational requirements of the problem. This has engendered the development of a rich variety of useful methods designed to answer specific questions at different levels of spatial, temporal, and energetic resolution. These methods fall largely into two classes: physically accurate, but computationally demanding methods and fast, approximate methods. We introduce here a new hybrid modeling tool, the Structured Intuitive Move Selector (SIMS), designed to bridge the divide between these two classes, while allowing the benefits of both to be seamlessly integrated into a single framework. This is achieved by applying a modern motion planning algorithm, borrowed from the field of robotics, in tandem with a well-established protein modeling library. SIMS can combine precise energy calculations with approximate or specialized conformational sampling routines to produce rapid, yet accurate, analysis of the large-scale conformational variability of protein systems. Several key advancements are shown, including the abstract use of generically defined moves (conformational sampling methods) and an expansive probabilistic conformational exploration. We present three example problems that SIMS is applied to and demonstrate a rapid solution for each. These include the automatic determination of ﾑﾑactiveﾒﾒ residues for the hinge-based system Cyanovirin-N, exploring conformational changes involving long-range coordinated motion between non-sequential residues in Ribose- Binding Protein, and the rapid discovery of a transient conformational state of Maltose-Binding Protein, previously only determined by Molecular Dynamics. For all cases we provide energetic validations using well-established energy fields, demonstrating this framework as a fast and accurate tool for the analysis of a wide range of protein flexibility problems

Techniques for modeling and analyzing RNA and protein folding energy landscapes

RNA and protein molecules undergo a dynamic folding process that is important to their function. Computational methods are critical for studying this folding pro- cess because it is difficult to observe experimentally. In this work, we introduce new computational techniques to study RNA and protein energy landscapes, includ- ing a method to approximate an RNA energy landscape with a coarse graph (map) and new tools for analyzing graph-based approximations of RNA and protein energy landscapes. These analysis techniques can be used to study RNA and protein fold- ing kinetics such as population kinetics, folding rates, and the folding of particular subsequences. In particular, a map-based Master Equation (MME) method can be used to analyze the population kinetics of the maps, while another map analysis tool, map-based Monte Carlo (MMC) simulation, can extract stochastic folding pathways from the map. To validate the results, I compared our methods with other computational meth- ods and with experimental studies of RNA and protein. I first compared our MMC and MME methods for RNA with other computational methods working on the com- plete energy landscape and show that the approximate map captures the major fea- tures of a much larger (e.g., by orders of magnitude) complete energy landscape. Moreover, I show that the methods scale well to large molecules, e.g., RNA with 200+ nucleotides. Then, I correlate the computational results with experimental findings. I present comparisons with two experimental cases to show how I can pre- dict kinetics-based functional rates of ColE1 RNAII and MS2 phage RNA and their mutants using our MME and MMC tools respectively. I also show that the MME and MMC tools can be applied to map-based approximations of protein energy energy landscapes and present kinetics analysis results for several proteins

Intelligent Motion Planning and Analysis with Probabilistic Roadmap Methods for the Study of Complex and High-Dimensional Motions

At first glance, robots and proteins have little in common. Robots are commonly thought of as tools that perform tasks such as vacuuming the floor, while proteins play essential roles in many biochemical processes. However, the functionality of both robots and proteins is highly dependent on their motions. In order to study motions in these two divergent domains, the same underlying algorithmic framework can be applied. This method is derived from probabilistic roadmap methods (PRMs) originally developed for robotic motion planning. It builds a graph, or roadmap, where configurations are represented as vertices and transitions between configurations are edges. The contribution of this work is a set of intelligent methods applied to PRMs. These methods facilitate both the modeling and analysis of motions, and have enabled the study of complex and high-dimensional problems in both robotic and molecular domains. In order to efficiently study biologically relevant molecular folding behaviors we have developed new techniques based on Monte Carlo solution, master equation calculation, and non-linear dimensionality reduction to run simulations and analysis on the roadmap. The first method, Map-based master equation calculation (MME), extracts global properties of the folding landscape such as global folding rates. On the other hand, another method, Map-based Monte Carlo solution (MMC), can be used to extract microscopic features of the folding process. Also, the application of dimensionality reduction returns a lower-dimensional representation that still retains the principal features while facilitating both modeling and analysis of motion landscapes. A key contribution of our methods is the flexibility to study larger and more complex structures, e.g., 372 residue Alpha-1 antitrypsin and 200 nucleotide ColE1 RNAII. We also applied intelligent roadmap-based techniques to the area of robotic motion. These methods take advantage of unsupervised learning methods at all stages of the planning process and produces solutions in complex spaces with little cost and less manual intervention compared to other adaptive methods. Our results show that our methods have low overhead and that they out-perform two existing adaptive methods in all complex cases studied